A computational cognitive agent capable of mathematical reasoning should be able to: (1) perform mental operations over abstract internal representations (e.g., counting numbers) and (2) perform physical operations over concrete external objects (e.g., counting apples). In a context of justification, both of these types of activity can contribute to mathematical explanations. In this paper, we focus on an agent's ability to enumerate external objects, the knowledge-level representational requirements (and side-effects) for such an ability, and the applicability of the enumeration result during an explanation. The SNePS knowledge-representation, reasoning, and acting system is used for a preliminary implementation of Cassie, our enumeration agent. The GLAIR architecture, which is used to model Cassie's embodiment, is also discussed.